How the tiniest words can impact casino house edge.
It’s strange how the smallest words can have such a large impact on the meaning of things. The difference between “now” and “not”, for example—a simple typo, but enormous difference in meaning. ‘We are now accepting new applications’, versus, ‘we are not accepting new applications’.
The same can be said of missing or misplaced punctuation. Where you place a comma, if you place one at all, when texting this statement to a loved one, can change a lot: “I’m not getting any better come home soon”.
Grammar is extremely important in all things—even gambling. Casinos use specific words to imply different meanings, and even the tiniest, seemingly innocent alterations can mean more than you think. For example, when reading a pay table, the difference between getting paid “to” or “for” your bet can have a great impact on the house edge.
What Is Casino House Edge?
The casino’s house edge is the amount of money the casino expects to win from its players. It is a percentage of all the money you wager. The percentage is determined by the rules, payouts and probabilities of the games you play.
For example, in American roulette, most wagers have a house edge of 5.26%. So, if you place $100 worth of $1 bets, you should expect to lose 5.26% of that, or $5.26. European roulette, on the other hand, has a 2.7% house edge. Betting $100 worth of $1 bets would give you a negative expectation of $2.70.
We come to this figure by dividing the ways to win a bet, by all possible outcomes, then multiplying that by the potential payout. Then, we add that to the dividend of the ways to lose and all possible outcomes, multiplied by the negative integer of the bet being risked.
That’s a lot to take in, I know. If you want a better understanding of calculating house edge, continue reading the next section. If not, skip on ahead to ‘How To and For Impacts Payouts‘.
How to Calculate House Edge
Let’s take a look at the formula:
[(Ways to Win / All Ways) * Potential Payout] + [(Ways to Lose / All Ways) * -Bet] = House Edge
Let’s give it a try… We’ll calculate a $10 bet on 1st Dozens (1-12), which pays 2 to 1 ($20). There are 12 outcomes that can win the bet, 26 outcomes that can lose, and 38 in all. So, the equation is:
[(12/38)*20] + [(26/38]*-10 =
Breaking that down, we get… (0.3158 *20) + (0.6842*-10) =
And breaking it down further… 6.316 + -6.842 = -0.526
0.526 converted into a percentage is –5.26%, meaning we can expect to a negative return of 5.26% (i.e. lose $5.26 per $100 bet).
In a European Roulette game, all wagers have a 2.7% house edge, thanks to the simple omission of the double-zero found in the American version. The formula is the same, except that all ways = 37 instead of 38. So, for a Dozens bet:
[(12/37)*20] + [(25/37]*-10 =
(0.3243*20) + (0.6757*-10) =
6.486 + -6.757 = -0.27 = 2.71%
How ‘To’ or ‘For’ Impact Payouts
The difference in “to” and “for” is what happens to your original bet. If you’re paid an amount “to” your $1 bet, you’ll get that wager back on top of the winnings. If you’re paid an amount “for” your $1 bet, you will only receive the winnings. The original bet won’t be returned.
It can be difficult to remember which is which, but think of it this way. If I offer you a loaf of bread “for” $1, I’m not going to give you the loaf of bread, and your dollar back. I’m going to keep that dollar in exchange for the bread. So when you see the word “for”, know that the casino is keeping that as payment for whatever you may get in return.
Knowing this is the first important step to making smart wagers. Knowing how it effects the casino’s edge is the second.
We talked about the payout for a Dozens bet in European roulette above. If the payout is “2 to 1” on a $1 bet, a winning bet receives $2, plus the $1 wagered, for a total $3 return. If the payout is “2 for 1”, the player receives only $2. The casino collects the original $1 bet. In this case, the player is only “winning” $1, not $2.
If you read and understand the casino house edge formula above, you’ll find that the edge increases from the usual 2.7% on a “2 to 1” bet, to a staggering 35.14%!
[(12/37)*10] + [(25/37]*-10 = -3.514
This is a rather extreme example, and one you won’t find in any real gambling situation. But it magnifies the difference between the simple terms “to” and “for”, and how important those two little words can be.
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